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In this paper we use convex analysis and variational inequality methods toestablish an existence result for a model of infinitesimal rate-independentgradient plasticity with kinematic hardening and plastic spin, in which thelocal backstress tensor remains symmetric. The model features a defect energycontribution which is quadratic in the dislocation density tensor Curl p,giving rise to nonlocal non-symmetric kinematic hardening. Use is made of arecently established Korn's type inequality for incompatible tensor fields. Thesolution space for the non-symmetric plastic distortion is naturally H(Curl)together with suitable tangential boundary conditions on the plasticdistortion. Connections to other models are established as well.

Existence results in dislocation based rate-independent isotropic  gradient plasticity with kinematical hardening and plastic spin: The case  with symmetric local backstress